Today, Friday, November 13, 2015 expressed as 11/13/15 is a sequential calendar date consisting of three consecutive odd numbers. 11/13/15 is the last one of its kind to occur in the 21^{st} century simply because the month number cannot exceed 12.

Last year’s sequential calendar date 12/13/14 was also the last one of its kind to occur in this century.

Sequential date 12/14/16 (even-number sequence) to occur next year will also be the last of its kind.

The following year’s 11/13/17 (prime-number sequence) will be the last one of its kind too.

Such century repeating sequential calendar dates written by using only the rightmost two digits of the year number are mostly clustered in the first quarter of each century due to the month-number constraint. Does this mean that the rest of the century will mostly be depleted from sequential calendar dates? No! We will explain.

Note that since sequential calendar dates don’t have a set definition, by being innovative and in some cases ignoring the dividers between the month, day, and year numbers, one can create many other sequential calendar dates consisting of sequential number series, some even to occur in the latter part of this century.

Here are examples of sequential calendar dates yet to occur, some of which prolong throughout the century:

Perfect square sequential calendar date 04/09/16 to occur next year consists of three consecutive square numbers. (Another such sequential date to occur later in the century will be 09/16/25.)

Sequential calendar date 8/15/17 to occur the following year is made of a Pythagorean triple 8, 15, and 17 since the sum of the squares of 8 and 15 equals the square of 17. (Another similar sequential date to occur later this century is 7/24/25.)

Sequential calendar date 06/12/18 interpreted as 1x6/2x6/3x6 represents a geometric series.

Next, sequential date 07/13/19 can be viewed as 6+1/2x6+1/3x6+1. Note also that 07, 13, and 19 are every other members of the prime-number sequence. Sequential date 10/13/19 to occur in the same year is made of three happy numbers, 10, 13 and 19 [1].

Sequential date 6/12/20 can be interpreted as 2x3/3x4/4x5. (Another such sequential date to occur in this century is 12/20/30.)

Sequential calendar date 4/3/21 consists of digits 1 to 4 in descending order. (Other such sequential dates to occur later in the century are 5/4/32, 6/5/43, 7/6/54, 8/7/65, 9/8/76, 10/9/87, and 11/10/98.) Same year, sequential date 08/13/21 consists of three consecutive Fibonacci numbers (08, 13, and 21).

Sequential calendar date 01/12/23 is made of two consecutive number sequences {0, 1, 2} and {1, 2, 3}, intertwined.

Sequential calendar date 02/06/24 is a factorial-number sequence (2!/3!/4!).

Sequential calendar dates 01/04/27 (1^{1}/2^{2}/3^{3}), 01/08/27 (cube-number sequence), and 03/09/27 (3^{1}/3^{2}/3^{3}) are all to occur in the same year. (Another sequential date similar to the last one will be 09/27/81, since it is 3^{2}/3^{3}/3^{4}.)

Sequential calendar date 1/7/29 consists of the digits of the Hardy-Ramanujan taxicab number, 1729 [2].

Sequential calendar date 7/5/31 consists of four odd-number digits appearing in descending order. (Another such sequential date will be 9/7/53.)

Sequential calendar date 08/16/32 (2^{3}/2^{4}/2^{5}) will be followed by 8/5/32, which is made of Fibonacci numbers 2, 3, 5, and 8, appearing in a descending order.

Sequential calendar date 11/22/33 to occur in 2033 is made of three consecutive palindrome numbers.

Sequential calendar date 1/2/34 consists of consecutive digits 1, 2, 3, and 4. (Other such sequential dates to occur are 2/3/45, 3/4/56, 4/5/67, 5/6/78, and 6/7/89.) This will be followed by 12/23/34, which is made of two consecutive number sequences {1, 2, 3} and {2, 3, 4} intertwined.

Sequential date 2/11/38 viewed without the dividers as 21138 consists of three descending-order Fibonacci numbers, 21, 13, and 8.

Sequential calendar date 8/6/42 is made of four even-numbered digits appearing in descending order.

Sequential calendar dates 01/23/45 and 12/3/45 to occur in the same year will each be unique.

Sequential calendar date 1/3/57 consists of odd digits 1, 3, 5, and 7. (Another such sequential date to occur is 3/5/79.)

Sequential calendar date 11/23/58 consists of the first six numbers (1, 1, 2, 3, 5, and 8) of the Fibonacci number series.

Sequential calendar date 02-09-64 corresponding to sequence 2^{1}/3^{2}/4^{3} will be followed by 04/16/64 (4^{1}/4^{2}/4^{3}) and 08/27/64 (cube-number sequence), all to occur in the same year.

Sequential calendar date 2/4/68 is made of even digits 2, 4, 6, and 8.

Sequential calendar date 01/08/81 can be interpreted as 1^{2}/2^{3}/3^{4}.

Sequential calendar date 1/3/85 consists of Fibonacci numbers 13, 8, and 5 (in descending order).

Sequential calendar dates are really fun and they indeed possess the power to tease our brains creatively and intellectually. In this article, we provided many different types of century repeating sequential calendar dates some extending throughout the century. We hope you can also create other sequential calendar dates to occur in this century.

[1] Happy number, Wikipedia

https://en.wikipedia.org/wiki/Happy_number

[2] 1729

https://en.wikipedia.org/wiki/1729_%28number%29

*Aziz Inan, Baris Inan and Cem Inan can be reached at ainan@up.edu, inan13@up.edu and inan16@up.edu respectively. *